Date: 12/19/95 at 18:0:5 From: Anonymous Subject: Books on Proofs Dear Dr. Math, Hi, I'm a fourth grader interested in learning how to do proofs. Can you recommend some good books on the different techniques used and how they are applied? It doesn't have to be only about geometry - I like algebra too. Thanks, Erin
Date: 6/17/96 at 9:46:17 From: Doctor Mike Subject: Re: Books on Proofs Erin, If we had been able to respond immediately, you could have put SOLVE IT! by James F. Fixx (1978, Doubleday) right at the top of your holiday gifts wish list. Also good, but in a totally different way, is MATH PROJECTS FOR YOUNG SCIENTISTS by David A. Thomas (1988, Franklin Watts). What a proof is depends on whether you are talking about math, science, law, politics, etc. Many good books on proof assume experience from high school or beyond. I recommend getting as much math-related experience as you can. Solving so-called word problems is best. Problem solving is really the first stage of developing an understanding of mathematical proof. That's why the Fixx book is so good. When you finally figure out a problem, you understand it and can explain it, and you just know by common sense that you are right. The PROJECTS book is more open-ended. Check in your library for titles concerning puzzles, brainteasers, paradoxes or mathematical recreations. Books you find by Martin Gardner or Raymond Smullyan also are worth a look. The Thomas Y. Crowell Co. has a YOUNG MATH BOOKS series of several dozen short books "on rather sophisticated subjects, introduced on an easy-to-understand enjoyable level for the youngest of mathematicians." I have seen several, and really like BASE FIVE by David Adler and LESS THAN NOTHING IS REALLY SOMETHING by Robert Froman. YES-NO; STOP-GO by Judith Gersting and Joseph Kuczkowski explains truth tables. This looks like a fine series. When you are ready to move on from practice in problem solving to studying the actual techniques of valid arguments and clearly presenting conclusive evidence, the paperback HOW TO READ AND DO PROOFS by Daniel Solow (1982, John Wiley) is excellent. It is well-written, but might be rough going without help from a teacher or a friend who already understands many of these ideas. Another math doctor suggested HOW TO SOLVE IT by George Polya (1957, Doubleday). -Doctor Mike, The Math Forum
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